Finite Group Databasebeta

← #8095673

Subgroups — #8095673

Order 512.

4518 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53089C214yesmaximal, complemented
2#53084C214yesmaximal, complemented
3#53083C214yesmaximal, complemented
4#53082C214yesmaximal, complemented
5#52314C218yesmaximal, complemented
6#46109C214yesmaximal, complemented
7#46078C214yesmaximal, complemented
8#46062C214yesmaximal, complemented
9#46019C214yesmaximal, complemented
10#45579C218yesmaximal, complemented
11#35627C211yesmaximal, characteristic, complemented
12#35584C211yesmaximal, characteristic
13#35555C211yesmaximal, characteristic, complemented
14#35540C211yesmaximal, characteristic
15#35529C211yesmaximal, characteristic, complemented
16#35529C211yesmaximal, characteristic, complemented
17#35330C211yesmaximal, characteristic, complemented
18#35275C211yesmaximal, characteristic, complemented
19#35266C211yesmaximal, characteristic, complemented
20#35266C211yesmaximal, characteristic, complemented
21#35151C211yesmaximal, characteristic, complemented
22#35151C211yesmaximal, characteristic, complemented
23#34814C211yesmaximal, characteristic, complemented
24#34814C211yesmaximal, characteristic, complemented
25C2×#2500C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#544C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C2×#518C2211yescharacteristic
31C22×#117C2211yescharacteristic
32#2868C2212yescomplemented
33#2862C2212yescomplemented
34#2860C2214yescomplemented
35#2860C2214yescomplemented
36#2859C2212yescomplemented
37#2859C2212yescomplemented
38#2855C2214yes—
39#2855C2214yes—
40#2838C2218yescomplemented
41#2837C2218yescomplemented
42#2837C2218yescomplemented
43#2832C2218yescomplemented
44#2831C2218yescomplemented
45#2830C2218yescomplemented
46#2827C2218yescomplemented
47#2823C2218yescomplemented
48#2820C2218yescomplemented
49#2814C2218yescomplemented
50#2793C2218yescomplemented
51#2777C2218yescomplemented
52#2773C2218yescomplemented
53#2770C2218yescomplemented
54#2765C2218yescomplemented
55#2759C2218yescomplemented
56#2745C2218yescomplemented
57#2731C2218yescomplemented
58#2729C2218yescomplemented
59#2727C2218yescomplemented
60#2725C2218yescomplemented
61#2723C2218yescomplemented
62#2718C2218yescomplemented
63#2716C2218yescomplemented
64#2715C2218yescomplemented
65#2707C2218yescomplemented
66#2702C2218yescomplemented
67#2690C2218yescomplemented
68#2689C2218yescomplemented
69#2674C2218yescomplemented
70#2660C2212yescomplemented
71#2660C2212yescomplemented
72#2660C2212yescomplemented
73#2660C2212yescomplemented
74#2644C2214yescomplemented
75#2644C2214yescomplemented
76#2626C2214yes—
77#2626C2214yes—
78#2571C2214yescomplemented
79#2570C2214yescomplemented
80#2570C2214yescomplemented
81#2566C2212yescomplemented
82#2566C2212yescomplemented
83#2566C2212yescomplemented
84#2566C2212yescomplemented
85#2563C2212yescomplemented
86#2563C2212yescomplemented
87#2561C2214yes—
88#2552C2214yescomplemented
89#2552C2214yescomplemented
90#2551C2214yescomplemented
91#2550C2214yescomplemented
92#2550C2214yescomplemented
93#2549C2218yes—
94#2542C2212yescomplemented
95#2542C2212yescomplemented
96#2513C2214yescomplemented
97#2513C2214yescomplemented
98#2512C2214yescomplemented
99#2512C2214yescomplemented
100#2509C2214yescomplemented
101#2508C2214yescomplemented
102#2507C2214yescomplemented
103#2506C2214yescomplemented
104#2505C2218yes—
105#2500C2214yes—
106#2500C2214yes—
107#2500C2214yes—
108#2500C2214yes—
109#2497C2212yescomplemented
110#2497C2212yescomplemented
111#2496C2212yescomplemented
112#2496C2212yescomplemented
113#2495C2212yescomplemented
114#2495C2212yescomplemented
115#2494C2212yescomplemented
116#2494C2212yescomplemented
117#2493C2214yes—
118#2493C2214yes—
119#2491C2214yes—
120#2491C2214yes—
121#2490C2214yes—
122#2490C2214yes—
123#2483C2214yes—
124#2480C2218yes—
125#2480C2218yes—
126#2480C2214yes—
127#2480C2214yes—
128#2473C2218yes—
129#2454C2214yescomplemented
130#2454C2214yescomplemented
131#2452C2214yescomplemented
132#2452C2214yescomplemented
133#2441C2214yescomplemented
134#2441C2214yescomplemented
135#2441C2214yescomplemented
136#2441C2214yescomplemented
137#2440C2218yes—
138#2439C2214yescomplemented
139#2439C2214yescomplemented
140#2439C2214yescomplemented
141#2439C2214yescomplemented
142#2437C2218yes—
143#2437C2218yes—
144#2435C2214yes—
145#2422C2214yes—
146#2422C2214yes—
147#2420C2214yes—
148#2420C2214yes—
149#2405C2214yes—
150#2401C2214yescomplemented
151#2401C2214yescomplemented
152C2×#394C2214yes—
153#2383C2218yescomplemented
154#2378C2218yescomplemented
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2317C2211yescharacteristic
160#2317C2211yescharacteristic
161#2316C2211yescharacteristic
162#2316C2211yescharacteristic
163#2309C2211yescharacteristic
164#2309C2211yescharacteristic
165#2309C2211yescharacteristic
166C4×#126C2214yescomplemented
167C4×#126C2214yescomplemented
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172C2×#390C2211yescharacteristic
173C2×#390C2211yescharacteristic
174C2×#388C2214yes—
175#2285C2211yescharacteristic
176#2285C2211yescharacteristic
177C2×#384C2211yescharacteristic
178C2×#382C2211yescharacteristic
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C23×D4C2311yescharacteristic
188C23×D4C2312yes—
189C24×C4C2311yescharacteristic
190#544—44no—
191#544—44no—
192#544—44no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2318yes—
200C2×#126C2314yes—
201C2×#126C2314yes—
202C2×#126C2318yes—
203C2×#126C2318yes—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2318yes—
211C2×#124C2318yes—
212C2×#123C2318yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×#121—44no—
219C2×#121C2314yes—
220C2×#121C2314yes—
221#518—44no—
222C2×C4×D4C2312yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×#117—44no—
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2314yes—
236C2×#117C2314yes—
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2314yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2314yes—
245C22×C22⋊C4C2314yes—
246C22×C22⋊C4C2314yes—
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2312yes—
250#401C2314yes—
251#401C2314yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#399C2318yes—
263#399C2318yes—
264#399C2318yes—
265#399C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#397C2318yes—
275#397C2314yes—
276#397C2318yes—
277#397C2314yes—
278#397C2318yes—
279#397C2314yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2314yes—
285#397C2314yes—
286#397C2314yes—
287#397C2318yes—
288#397C2318yes—
289#396C2314yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2314yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#393C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#391C2318yes—
319#391C2318yes—
320#391C2318yes—
321#391C2318yes—
322#390C2312yes—
323#390C2312yes—
324#390C2312yes—
325#390C2312yes—
326#390C2312yes—
327#390C2312yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2312yes—
333#390C2312yes—
334#390C2318yes—
335#390C2314yes—
336#390C2314yes—
337#389C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2318yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2312yes—
358#389C2312yes—
359#389C2318yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#386C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2314yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2314yes—
405#385C2314yes—
406#385C2318yes—
407#385C2314yes—
408#385C2314yes—
409#385C2314yes—
410#385C2314yes—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2312yes—
414#384C2312yes—
415#384C2318yes—
416#384C2312yes—
417#384C2314yes—
418#384C2312yes—
419#384C2312yes—
420#384C2312yes—
421#384C2311yescharacteristic
422#384C2312yes—
423#384C2311yescharacteristic
424#384C2312yes—
425#383C2314yes—
426#383C2314yes—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2312yes—
430#382C2312yes—
431#382C2318yes—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2312yes—
435#382C2314yes—
436#382C2312yes—
437#382C2312yes—
438#382C2312yes—
439#382C2312yes—
440#382C2312yes—
441#381C2312yes—
442#381C2312yes—
443#381C2312yes—
444#381C2312yes—
445#381C2318yes—
446#380C2318yes—
447#380C2318yes—
448#380C2314yes—
449#380C2314yes—
450#380C2312yes—
451#380C2312yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2314yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#379C2314yes—
461#379C2314yes—
462#379C2314yes—
463#379C2312yes—
464#379C2312yes—
465#379C2312yes—
466#379C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492#376C2312yes—
493#376C2312yes—
494C2×#95C2314yes—
495C2×#95C2312yes—
496C43C2312yes—
497C43C2312yes—
498C25C2412yes—
499C25C2411yescharacteristic
500C22×Q8C2414yes—
501C22×Q8C2414yes—
502C22×Q8C2414yes—
503C22×D4—24no—
504C22×D4—24no—
505C22×D4—24no—
506C22×D4—44no—
507C22×D4—84no—
508C22×D4C2412yes—
509C22×D4C2412yes—
510C22×D4C2418yes—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4C2411yescharacteristic
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2414yes—
523C23×C4C2414yes—
524C23×C4C2411yescharacteristic
525C4⋊Q8—44no—
526C4⋊Q8—44no—
527C4⋊Q8—44no—
528C4⋊Q8—44no—
529C4⋊Q8—44no—
530C4⋊Q8—44no—
531C4⋊Q8—88no—
532#126—416no—
533#126—48no—
534#126—48no—
535#126—88no—
536#125—44no—
537#125—44no—
538#125—44no—
539#125—44no—
540#125—44no—
541#125—44no—
542#125—88no—
543#124—88no—
544#123—88no—
545C22⋊Q8—48no—
546C22⋊Q8—48no—
547C22⋊Q8—48no—
548C22⋊Q8—416no—
549C22⋊Q8—88no—
550#121—48no—
551#121—48no—
552C4×D4—44no—
553C4×D4—44no—
554C4×D4—44no—
555C4×D4—44no—
556#117—24no—
557#117—24no—
558#117—24no—
559#117—24no—
560#117—24no—
561#117—24no—
562#117—24no—
563#117—24no—
564#117—48no—
565#117—48no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—24no—
569C2×C4⋊C4—84no—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C22⋊C4—48no—
620C2×C22⋊C4—44no—
621C2×C22⋊C4—48no—
622C2×C22⋊C4—44no—
623C2×C22⋊C4—44no—
624C2×C22⋊C4—84no—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C42—24no—
660C2×C42—24no—
661C2×C42—44no—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2414yes—
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2418yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2414yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2418yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721C24—22no—
722C24—24no—
723C24—22no—
724C24—22no—
725C24—24no—
726C24—24no—
727C24—42no—
728C24—42no—
729C24—44no—
730C24—44no—
731C24C2512yes—
732C24C2514yes—
733C24C2511yescharacteristic
734C2×Q8—44no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—48no—
738C2×Q8—48no—
739C2×Q8—48no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—416no—
750C2×D4—816no—
751C22×C4—22no—
752C22×C4—24no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—44no—
769C22×C4—42no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—416no—
777C22×C4H(5,𝔽2)14yes—
778C22×C42−1+414yes—
779C22×C42−1+414yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—48no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—216no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—42no—
863C22⋊C4—42no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—22no—
890C42—24no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—28no—
900C42—48no—
901C42—48no—
902C42—44no—
903C42—44no—
904C42—44no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—24no—
909C23—22no—
910C23—22no—
911C23—24no—
912C23—24no—
913C23—22no—
914C23—22no—
915C23—28no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—44no—
920C23—44no—
921C23—44no—
922C23—48no—
923C23—84no—
924C23—84no—
925C23—84no—
926C23—84no—
927C23—88no—
928C23—88no—
929C23C2×H(5,𝔽2)12yes—
930C23C2×2−1+412yes—
931C23C2×2−1+412yes—
932C23C2611yescharacteristic
933Q8—164no—
934Q8—164no—
935Q8—164no—
936D4—48no—
937D4—48no—
938D4—816no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—28no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—22no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—48no—
988C2×C4—44no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—84no—
994C2×C4—84no—
995C2×C4—164no—
996C2×C4—164no—
997C2×C4#563116yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4C2×2−1+412yes—
1001C2×C4C2×2−1+412yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4#58514yes—
1005C22—22no—
1006C22—22no—
1007C22—24no—
1008C22—24no—
1009C22—44no—
1010C22—42no—
1011C22—44no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—48no—
1016C22—42no—
1017C22—44no—
1018C22—42no—
1019C22—42no—
1020C22—48no—
1021C22—88no—
1022C22—168no—
1023C22C2×#56314yes—
1024C22C22×H(5,𝔽2)11yescharacteristic
1025C22C22×2−1+411yescharacteristic
1026C22C22×2−1+411yescharacteristic
1027C22C2×#58512yes—
1028C22H(7,𝔽2)12yes—
1029C4—24no—
1030C4—42no—
1031C4—44no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—44no—
1036C4—44no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—44no—
1042C4—44no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—44no—
1047C4—44no—
1048C4—42no—
1049C4C2×#56314yes—
1050C4C2×#56314yes—
1051C2—24no—
1052C2—82no—
1053C2—84no—
1054C2C22×#56311yescharacteristic
1055C2#6283611yescharacteristic
1056C2#6287611yescharacteristic
1057C2#6292912yes—
1058C2#6295812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53089C2semidirect
2. #53084C2semidirect
3. #53083C2semidirect
4. #53082C2semidirect
5. #52314C2semidirect
6. #46109C2semidirect
7. #46078C2semidirect
8. #46062C2semidirect
9. #46019C2semidirect
10. #45579C2semidirect
11. #35627C2semidirect
13. #35555C2semidirect
15. #35529C2semidirect
16. #35529C2semidirect
17. #35330C2semidirect
18. #35275C2semidirect
19. #35266C2semidirect
20. #35266C2semidirect
21. #35151C2semidirect
22. #35151C2semidirect
23. #34814C2semidirect
24. #34814C2semidirect
32. #2868C22semidirect
33. #2862C22semidirect
34. #2860C22semidirect
35. #2860C22semidirect
36. #2859C22semidirect
37. #2859C22semidirect
40. #2838C22semidirect
41. #2837C22semidirect
42. #2837C22semidirect
43. #2832C22semidirect
44. #2831C22semidirect
45. #2830C22semidirect
46. #2827C22semidirect
47. #2823C22semidirect
48. #2820C22semidirect
49. #2814C22semidirect
50. #2793C22semidirect
51. #2777C22semidirect
52. #2773C22semidirect
53. #2770C22semidirect
54. #2765C22semidirect
55. #2759C22semidirect
56. #2745C22semidirect
57. #2731C22semidirect
58. #2729C22semidirect
59. #2727C22semidirect
60. #2725C22semidirect
61. #2723C22semidirect
62. #2718C22semidirect
63. #2716C22semidirect
64. #2715C22semidirect
65. #2707C22semidirect
66. #2702C22semidirect
67. #2690C22semidirect
68. #2689C22semidirect
69. #2674C22semidirect
70. #2660C22semidirect
71. #2660C22semidirect
72. #2660C22semidirect
73. #2660C22semidirect
74. #2644C22semidirect
75. #2644C22semidirect
78. #2571C22semidirect
79. #2570C22semidirect
80. #2570C22semidirect
81. #2566C22semidirect
82. #2566C22semidirect
83. #2566C22semidirect
84. #2566C22semidirect
85. #2563C22semidirect
86. #2563C22semidirect
88. #2552C22semidirect
89. #2552C22semidirect
90. #2551C22semidirect
91. #2550C22semidirect
92. #2550C22semidirect
94. #2542C22semidirect
95. #2542C22semidirect
96. #2513C22semidirect
97. #2513C22semidirect
98. #2512C22semidirect
99. #2512C22semidirect
100. #2509C22semidirect
101. #2508C22semidirect
102. #2507C22semidirect
103. #2506C22semidirect
109. #2497C22semidirect
110. #2497C22semidirect
111. #2496C22semidirect
112. #2496C22semidirect
113. #2495C22semidirect
114. #2495C22semidirect
115. #2494C22semidirect
116. #2494C22semidirect
129. #2454C22semidirect
130. #2454C22semidirect
131. #2452C22semidirect
132. #2452C22semidirect
133. #2441C22semidirect
134. #2441C22semidirect
135. #2441C22semidirect
136. #2441C22semidirect
138. #2439C22semidirect
139. #2439C22semidirect
140. #2439C22semidirect
141. #2439C22semidirect
150. #2401C22semidirect
151. #2401C22semidirect
153. #2383C22semidirect
154. #2378C22semidirect
166. C4×#126C22semidirect
167. C4×#126C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#530892
#530842
#530832
#530822
#523142
#461092
#460782
#460622
#460192
#455792
#356272
#355842
#355552
#355402
#355292
#353302
#352752
#352662
#351512
#348142
C2×#25002